Problem: Simplify to lowest terms. $\dfrac{110}{66}$
Explanation: There are several ways to tackle this problem. What is the greatest common factor (GCD) of 110 and 66? $110 = 2\cdot5\cdot11$ $66 = 2\cdot3\cdot11$ $\mbox{GCD}(110, 66) = 2\cdot11 = 22$ $\dfrac{110}{66} = \dfrac{5 \cdot 22}{ 3\cdot 22}$ $\hphantom{\dfrac{110}{66}} = \dfrac{5}{3} \cdot \dfrac{22}{22}$ $\hphantom{\dfrac{110}{66}} = \dfrac{5}{3} \cdot 1$ $\hphantom{\dfrac{110}{66}} = \dfrac{5}{3}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{110}{66}= \dfrac{2\cdot55}{2\cdot33}= \dfrac{2\cdot 11\cdot5}{2\cdot 11\cdot3}= \dfrac{5}{3}$